Circular Motion Standard 9

Distance travelled = 2πr Circular Motion Object moves around a circular path. If the speed remains constant then it is called as uniform circular motion. Such a body is always accelerating because there is a constant change in the direction of motion. e.g. motion of earth around the sun Distance travelled = 2πr Speed = Distance / Time

Circular Motion - Equations vt Radius = r m Distance travelled in one rotation = 2Π𝑟 m Time for one rotation = T s Speed (v) = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆 = 𝟐𝜫𝒓 𝑻 𝒎/𝒔 In a small time interval t, the object covers 𝑣𝑡 m. By Pythagoras theorem – (𝑟+𝑥) 2 = 𝑟 2 + (𝑣𝑡) 2 ∴ 𝑟 2 +2𝑟𝑥+ 𝑥 2 = 𝑟 2 + (𝑣𝑡) 2 Since x is very small, 𝑥 2 is even smaller. ∴ 2𝑟𝑥 = (𝑣𝑡) 2 ∴ 𝑥 = 1 2𝑟 (𝑣𝑡) 2 Comparing with 2nd equation of motion 𝑠=𝑢𝑡+ 1 2 𝑎 𝑡 2 𝑚 𝐚= 𝒗 𝟐 𝒓 𝐦/ 𝒔 𝟐 x Radius = r r